What is the solution of 82.78(p+11.892)=72.8464 when solving for p? Do not round

Answer 1

To solve the equation \( 82.78(p + 11.892) = 72.8464 \) for \( p \), follow these steps:

1. Distribute \( 82.78 \) on the left side: \[ 82.78p + 82.78 \cdot 11.892 = 72.8464 \] Calculate \( 82.78 \cdot 11.892 \): \[ 82.78 \cdot 11.892 = 984.79456 \] So, the equation now looks like: \[ 82.78p + 984.79456 = 72.8464 \]

2. Isolate the term with \( p \): Subtract \( 984.79456 \) from both sides: \[ 82.78p = 72.8464 - 984.79456 \] Now calculate \( 72.8464 - 984.79456 \): \[ 72.8464 - 984.79456 = -911.94816 \] So, we have: \[ 82.78p = -911.94816 \]

3. Solve for \( p \): Divide both sides by \( 82.78 \): \[ p = \frac{-911.94816}{82.78} \] Now calculate \( \frac{-911.94816}{82.78} \): \[ p \approx -11.002 \] (Be sure to use exact values depending on your calculator's capabilities, as this final value may not be rounded).

Thus, the solution for \( p \) is: \[ p = \frac{-911.94816}{82.78} \] This does not round it; it's the exact answer before rounding.